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STATISTICAL DISTRIBUTION OF WAVE HEIGHTS IN CORRELATION WITH ENERGY SPECTRA AND WATER DEPTH

This paper discusses specific aspects of a study being conducted in the southwestern part of the Netherlands with regard to coastal morphology and the design of coastal structures. The main part of this study examines the statistical distribution of wave heights in relation to the height of the sea surface at fixed points as a function of time, the water depth, and the energy spectrum of the wave motion. The results of theoretical studies by D.E. Cartwright and M.S. Longuet-Higgins and data on wave measurements obtained by Rijkswaterstaat in the North Sea were used. The theoretical frequency distributions of the wave heights, derived by Cartwright and Longuet-Higgins for the linear model are based on the assumption that the distribution of the ordinates of the sea surface as a function of time is Gaussian. A brief description is given of the linear model and its limitations. The deviations of frequency distributions of the sea surface from those of the linear model are examined. The wave heights are described in terms of four parameters and the distributions of these four wave height parameters are considered as a function of the standard deviation, the skewness of the sea surface distribution, and the relative width of the energy spectrum. From the frequency distributions obtained from observations, the quotients of the significant wave heights are determined as a function of the relative width and skewness variables. The wave height parameters are further examined following the foregoing formulations. Based on this study, the authors concluded that the statistical distribution of wave heights in relatively shallow water apparently depends on the standard deviation of the distribution of the sea surface ordinates, the relative width of the energy spectrum, and the relation between the wave length, the mean energy and the water depth.

Supplemental Notes:

Presented at the 9th Conference on Coastal Engineering, Lisbon, Portugal. Chapter 8 of the Conference Proceedings.